# Theoretical and Actual Acceleration for an Atwood Machine

• Pandaluvv2
In summary, the conversation involved discussing the calculation of acceleration and tension using free body diagrams and equations involving mass, gravity, and acceleration. Two trials were conducted, with the first one needing assistance. The formulas used were A=(m2-m1/m1+m2)g for acceleration, Ath=g(m2-m1/m1+m2) for theoretical acceleration, and T=(2m1m2/m1+m2)g for tension. It was clarified that the units should be in kilograms for consistency.

## Homework Statement

Include free body diagrams and equations solved independently for acceleration and tension. Note: a and T are to be expressed in terms of m1, m2, and g only.
Trial 1:Mass1= 55g and Mass2= 60g
Trial 2:Mass1= 55g and Mass2= 65g
We are doing 2 trials but i need help with the first one. I'm not sure how to figure out the acceleration and theoretical acceleration, should they be coming out the same?

## Homework Equations

A=(m2-m1/m1+m2)g
Ath=g(m2-m1/m1+m2)
T=(2m1m2/m1+m2)g

## The Attempt at a Solution

Trial 1: A=((60-55)/(60+55))*9.8 = (5/115)*9.8 = 0.426m/s/s
Ath=9.8*((60-55)/(60+55)) = 9.8*(5/115) = 0.4260m/s/s
T=(2*55*60/55+60)9.8 = (6600/115)*9.8 = 562.43N

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Hi Pandaluvv2, welcome to Physics Forums.

Is this assignment accompanying a hands-on lab? If so, the "actual acceleration" would be the value you measure during the experiment, which would subsequently be compared to the theoretical value that you calculate.

The formulas that you've arrived at appear to be okay but you need to be careful with the units. Your masses are given in grams but should be converted to kilograms for use in the tension formula. The scaling factors happen to cancel out in the acceleration formula so your result turns out to be correct, but you should be using kilograms there too.

Okay, that makes sense, I forgot we had found acceleration during class, which would have saved me a bunch of time. The only thing I should change is my mass to kilograms then right? So I can use it for the tension?

Pandaluvv2 said:
Okay, that makes sense, I forgot we had found acceleration during class, which would have saved me a bunch of time. The only thing I should change is my mass to kilograms then right? So I can use it for the tension?

Yup. Work in kilograms.

Okay, thank you very much for the help!